PHOENIX — A bill that would let more Arizona employers drop coverage for birth control drugs stalled Monday in the state Senate because of increasing opposition from women who feared they would have to reveal private health information to employers.

But supporters said they're willing to make changes to address such concerns voiced by Gov. Jan Brewer, who said the bill could create a potentially uncomfortable situation for women, and others including U.S. Sen. John McCain.

The changes would include reassurances that employers won't get information about workers' private health care information, said Cathi Herrod, a leader of an advocacy group for social conservatives that is lobbying for the bill along with Catholic bishops.

Under the bill, employers with religious or moral objections could decline to provide employees with coverage for birth control drugs being used to avoid pregnancy. Only religious entities such as churches now have that right in Arizona.

Coverage to use the drugs for medical purposes other than avoiding pregnancy, such as treatment for acne, still would be provided through a reimbursement process, but employers could require that workers provide evidence that the drugs aren't being sought for avoiding pregnancy.

Critics say employers could force workers to disclose their personal medical circumstances in order to get reimbursements. Herrod, president of the Center for Arizona Policy, disputed that employers would get that information.

Brewer, a Republican, said Friday she didn't have a position on the bill, but she expressed unease that it could result in women having to disclose private medical information to employers.

On Sunday, McCain, R-Ariz., also voiced reservations about the bill, saying Republicans should focus on jobs and the economy and not allow critics to paint Republicans as waging a war on women.

Arizona Senate President Steve Pierce pulled the bill from a Senate committee agenda Monday. Spokesman Mike Philipsen cited Brewer's comments and objections from members of the public.

Philipsen said Pierce's move doesn't mean the bill is dead, but at a minimum, the move delays its consideration by the full Senate.

Herrod said any information workers provide to get reimbursements would go only to the health plans.

However, the legislation isn't clear on that. Some provisions of the bill specify that evidence would be submitted to the insurer or health plan, but at least one other provision specifies that the reimbursement claim and evidence would go to the company opting out of coverage for avoiding pregnancy.

A health law expert said workers can be required to waive privacy rights and allow employers to have the information in order to get reimbursements.

"It's not unusual for the employer to have to ask for medical confirmation of specific things," said James G. Hodge, an Arizona State University professor who specializes in health law and ethics.

In many cases, an employee already has to plead for coverage of a type of care, such as when an insurer denies coverage and tells the worker to take it up with her employer, he said. "If she wants reimbursement, legally she is going to have to waive privacy interests."

Herrod said the planned amendment to change the bill hadn't been written yet, but it would be intended to make sure any information goes to the insurer but not to the employer.

"The employer would not be able to coerce the employee into waiving any of this," she said.

Herrod said she expects Brewer and McCain won't stand as roadblocks to the bill and that it will enjoy strong support from the Senate "once the facts are clear."

The current bill has already been approved by the House, but the bill would have to return there if the Senate makes any changes.